FORTUNE — Dear Annie: At the end of your recent column about cultural “fit,” the expert you quoted said that most job candidates don’t ask enough questions. But what should interviewees ask, especially when talking with a prospective boss? I’m now in my second job since graduating from college in 2006 and, while my boss and I get along all right most of the time, I can’t help feeling like we don’t connect very well or really understand each other. Part of it might be that we just don’t have that much in common, so I find myself explaining things about my approach to my work that I think would be self-evident if our backgrounds were more similar. I’m not job hunting right now but, in case I decide to make a move, are there specific questions people can ask in a job interview to determine whether they and a potential boss are a good match? — Curious in California
Dear Curious: Indeed there are, and the answers can help you pinpoint how effectively you could work with a given boss, or even how long you will stay in the job. “People join companies, but they leave managers,” says Kathy Harris, managing director at New York City-based financial and IT executive search firm Harris Allied. “Even great perks like onsite gyms and free lunches can’t make up for a boss who isn’t engaged with, or supportive of, his or her people.”
Harris suggests three questions you could ask in your next interview (whenever that may be), beginning with one you might wish you had thought of before taking the job you have now. “At an appropriate point in the conversation, ask your potential boss to tell you about his background,” she says. “Listen for experiences that match yours. For instance, did the person come up through the ranks in a hands-on role similar to yours? How long has it been since she worked as an individual contributor?”
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Of course, everyone’s career is a little bit different but, as you’ve noticed, it can be hard to communicate with someone who has never stood in your shoes, or who did your current work so long ago that the issues and challenges involved have been lost in the past.
Second, says Harris, “ask yourself some critical questions about the person you’ll be working for. What do you hope to learn from this boss? Can you see him or her as a coach or a mentor? It’s often difficult to work for long with a manager who has little professional value to bring to the relationship.”
Then, Harris advises, “Ask about the key attributes they’re looking for. What would a successful candidate bring to the job? Answers like ‘thick-skinned’ and ‘able to push back’ may mean this boss will be difficult to work with.” Not that that’s always a bad thing: “Challenging bosses have been known to bring out the best in their people if their personalities and styles mesh well,” Harris notes. But if a manager sees herself as highly demanding and is willing to admit it (or even brag about it), you’re far better off knowing that ahead of time than having it come as a surprise.
Another way to ferret out the same information is to ask the manager to describe his favorite underlings, past or present. “A question like, ‘Can you tell me about the characteristics and behaviors of an employee who met or exceeded your expectations?’ will give you some useful insights into what this manager values most,” says Lois Frankel, head of Pasadena-based Corporate Coaching International. “If the response is, ‘They worked every night until 8 p.m. to get the job done, without complaining,’ and you value time with your family, then you know it won’t be a good fit.”
A fifth question, Frankel says: “Ask if you can speak with one or two others who report to this person. Something like, ‘Can you tell me what you like best, and what you like least, about working for this boss and this company?’ should help you get the answers you need to make an informed decision.”
One more thing that will tell you a lot, Frankel adds, is simply paying attention to nonverbal cues like how this manager’s office is decorated. “For example, let’s say you consider yourself a ‘people person’ who’s motivated to do your best work when you have warm, collegial relationships with colleagues,” she says. “If a prospective boss’s office is devoid of anything personal — like family photos or even pictures of a pet, memorabilia, or anything else non-work-related — this may be a clue that you’re unlikely to connect in a way that will bring out the best in you.”
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In this iffy job market, can you really afford to be so picky? Frankel believes you can’t afford not to be. “Too often, people are so intent on landing the job, they aren’t concerned enough with ensuring the right fit, which is critical for success,” she says. “Even in this tough economy, being selective is important if you don’t want to end up hopping from one job to another” — or stuck in one where you can’t really shine.
Talkback: What questions have you asked in job interviews that gave you a clear sense of what it would be like to work for a particular boss? Which questions do you wish you’d asked? Leave a comment below.